scholarly journals Revisiting Gaussian copulas to handle endogenous regressors

2021 ◽  
Author(s):  
Jan-Michael Becker ◽  
Dorian Proksch ◽  
Christian M. Ringle
Keyword(s):  
Regression Models ◽  
Statistical Power ◽  
Multilevel Models ◽  
Gaussian Copula ◽  
Simulation Studies ◽  
Validity Of Results ◽  
Endogenous Regressors ◽  
Copula Approach ◽  
Original Presentation ◽  
And Performance

AbstractMarketing researchers are increasingly taking advantage of the instrumental variable (IV)-free Gaussian copula approach. They use this method to identify and correct endogeneity when estimating regression models with non-experimental data. The Gaussian copula approach’s original presentation and performance demonstration via a series of simulation studies focused primarily on regression models without intercept. However, marketing and other disciplines’ researchers mainly use regression models with intercept. This research expands our knowledge of the Gaussian copula approach to regression models with intercept and to multilevel models. The results of our simulation studies reveal a fundamental bias and concerns about statistical power at smaller sample sizes and when the approach’s primary assumptions are not fully met. This key finding opposes the method’s potential advantages and raises concerns about its appropriate use in prior studies. As a remedy, we derive boundary conditions and guidelines that contribute to the Gaussian copula approach’s proper use. Thereby, this research contributes to ensuring the validity of results and conclusions of empirical research applying the Gaussian copula approach.

Accounting for Endogeneity in Regression Models Using Copulas: A Step-by-Step Guide for Empirical Studies

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alecos Papadopoulos
Keyword(s):  
Regression Models ◽  
Empirical Studies ◽  
Gaussian Copula ◽  
Supplementary File ◽  
Linear Regression Models ◽  
Finite Samples ◽  
Endogenous Regressors ◽  
Proposed Model ◽  
Present Simulation ◽  
Detailed Presentation

Abstract We provide a detailed presentation and guide for the use of Copulas in order to account for endogeneity in linear regression models without the need for instrumental variables. We start by developing the model from first principles of likelihood inference, and then focus on the Gaussian Copula. We discuss its merits and propose diagnostics to assess its validity. We analyze in detail and provide solutions to the various issues that may arise in empirical applications for applying the method. We treat the cases of both continuous and discrete endogenous regressors. We present simulation evidence for the performance of the proposed model in finite samples, and we illustrate its application by a short empirical study. A Supplementary File contains additional simulations and another empirical illustration.

Replication of the Superstition and Performance Study by

2014 ◽  
Vol 45 (3) ◽  
pp. 239-245 ◽  
Author(s):  
Robert J. Calin-Jageman ◽  
Tracy L. Caldwell
Keyword(s):  
Task Difficulty ◽  
Statistical Power ◽  
Meta Analysis ◽  
A Priori ◽  
Significant Heterogeneity ◽  
Performance Study ◽  
Improve Performance ◽  
Research Designs ◽  
Series Of Experiments ◽  
And Performance

A recent series of experiments suggests that fostering superstitions can substantially improve performance on a variety of motor and cognitive tasks ( Damisch, Stoberock, & Mussweiler, 2010 ). We conducted two high-powered and precise replications of one of these experiments, examining if telling participants they had a lucky golf ball could improve their performance on a 10-shot golf task relative to controls. We found that the effect of superstition on performance is elusive: Participants told they had a lucky ball performed almost identically to controls. Our failure to replicate the target study was not due to lack of impact, lack of statistical power, differences in task difficulty, nor differences in participant belief in luck. A meta-analysis indicates significant heterogeneity in the effect of superstition on performance. This could be due to an unknown moderator, but no effect was observed among the studies with the strongest research designs (e.g., high power, a priori sampling plan).

scholarly journals The Implications of Regulatory Framework for Topical Semisolid Drug Products: From Critical Quality and Performance Attributes towards Establishing Bioequivalence

Pharmaceutics ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 710
Author(s):  
Tanja Ilić ◽  
Ivana Pantelić ◽  
Snežana Savić
Keyword(s):  
Statistical Power ◽  
Failure Modes ◽  
In Vitro Release ◽  
Optimal Number ◽  
Drug Products ◽  
Pharmaceutical Equivalence ◽  
And Performance ◽  
Low Sensitivity

Due to complex interdependent relationships affecting their microstructure, topical semisolid drug formulations face unique obstacles to the development of generics compared to other drug products. Traditionally, establishing bioequivalence is based on comparative clinical trials, which are expensive and often associated with high degrees of variability and low sensitivity in detecting formulation differences. To address this issue, leading regulatory agencies have aimed to advance guidelines relevant to topical generics, ultimately accepting different non-clinical, in vitro/in vivo surrogate methods for topical bioequivalence assessment. Unfortunately, according to both industry and academia stakeholders, these efforts are far from flawless, and often upsurge the potential for result variability and a number of other failure modes. This paper offers a comprehensive review of the literature focused on amending regulatory positions concerning the demonstration of (i) extended pharmaceutical equivalence and (ii) equivalence with respect to the efficacy of topical semisolids. The proposed corrective measures are disclosed and critically discussed, as they span from mere demands to widen the acceptance range (e.g., from ±10% to ±20%/±25% for rheology and in vitro release parameters highly prone to batch-to-batch variability) or reassess the optimal number of samples required to reach the desired statistical power, but also rely on specific data modeling or novel statistical approaches.

scholarly journals On the control of the difference between two Brownian motions: a dynamic copula approach

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Thomas Deschatre
Keyword(s):  
Cumulative Distribution Function ◽  
Survival Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Gaussian Copula ◽  
Brownian Motions ◽  
Dynamic Copula ◽  
Copula Approach ◽  
The Difference ◽  
The Right

AbstractWe propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Considering two Brownian motions B1t and B2t, the main result is that the range of possible values for is the same for Markovian pairs and all pairs of Brownian motions, that is with φ being the cumulative distribution function of a standard Gaussian random variable.

scholarly journals Z-Curve

2017 ◽  
Author(s):  
Ulrich Schimmack ◽  
Jerry Brunner
Keyword(s):  
Selection Bias ◽  
Statistical Power ◽  
False Negative ◽  
Simulation Studies ◽  
Replication Studies ◽  
Negative Results ◽  
False Negative Results ◽  
Selection For ◽  
Z Curve ◽  
Substantial Heterogeneity

In recent years, the replicability of original findings published in psychology journals has been questioned. A key concern is that selection for significance inflates observed effect sizes and observed power. If selection bias is severe, replication studies are unlikely to reproduce a significant result. We introduce z-curve as a new method that can estimate the average true power for sets of studies that are selected for significance. We compare this method with p-curve, which has been used for the same purpose. Simulation studies show that both methods perform well when all studies have the same power, but p-curve overestimates power if power varies across studies. Based on these findings, we recommend z-curve to estimate power for sets of studies that are heterogeneous and selected for significance. Application of z-curve to various datasets suggests that the average replicability of published results in psychology is approximately 50%, but there is substantial heterogeneity and many psychological studies remain underpowered and are likely to produce false negative results. To increase replicability and credibility of published results it is important to reduce selection bias and to increase statistical power.

scholarly journals Disparities in injury morbidity among young adults in the USA: individual and contextual determinants

2018 ◽  
Vol 72 (6) ◽  
pp. 458-464 ◽  
Author(s):  
Susanne Schmidt ◽  
P Johnelle Sparks
Keyword(s):  
Young Adults ◽  
Conceptual Framework ◽  
Regression Models ◽  
Injury Risk ◽  
College Graduates ◽  
Multilevel Models ◽  
Health Behaviours ◽  
Population Data ◽  
Multilevel Regression ◽  
Logistic Regression Models

BackgroundInjuries have been recognised as important public health concerns, particularly among adolescents and young adults. Few studies have examined injuries using a multilevel perspective that addresses individual socioeconomic status (SES) and health behaviours and local socioeconomic conditions in early adolescence. We offer a conceptual framework incorporating these various components.MethodsWe test our conceptual framework using population data from the National Longitudinal Study of Adolescent Health Wave 4 when respondents were young adults and linked them to contextual level data from when they were middle-schoolers. We use logistic and multilevel regression models to examine self-reported injury risk in young adults by sex (n=14 356).ResultsLogistic regression models showed that men were more likely to experience serious injuries than women (OR 1.75, P<0.0001), but SES and health behaviours operated differently by sex. In stratified models, men with lower education had consistently higher injury risk, while only women with some college had increased injury risk (OR 1.40, P=0.0089) than college graduates. Low household income (OR 1.54, P=0.0011) and unemployment (OR 1.50, P=0.0008) increased female injury risk, but was non-significant for men. Alcohol consumption increased injury risk for both sexes, while only female smokers had elevated injury risk (OR 1.38, P=0.0154). In multilevel models, significant county-level variation was only observed for women. Women living in disadvantaged neighbourhoods during adolescence had increased injury risk (OR 1.001, P<0.0001).ConclusionsThese findings highlight the importance of investigating mechanisms that link early-life contextual conditions to early adult SES and health behaviours and their linkage to injury risk, particularly for women.

EXPRESS: Handling Endogenous Regressors using Copulas: A Generalization to Linear Panel Models with Fixed Effects and Correlated Regressors

2021 ◽  
pp. 002224372110708
Author(s):  
Rouven E. Haschka
Keyword(s):  
Fixed Effects ◽  
Estimation Method ◽  
Copula Function ◽  
Small Time ◽  
Joint Estimation ◽  
Gaussian Copula ◽  
Correlated Errors ◽  
Finite Sample ◽  
Panel Models ◽  
Endogenous Regressors

This paper proposes a panel data generalization for a recently suggested IVfree estimation method that builds on joint estimation. The author shows how the method can be extended to linear panel models by combining fixed-effects transformations with the common GLS transformation to allow for heterogeneous intercepts. To account for between-regressor dependence, the author proposes determining the joint distribution of the error term and all explanatory variables using a Gaussian copula function, with the distinction that some variables are endogenous and the others are exogenous. The identification does not require any instrumental variables if the regressor-error relation is nonlinear. With a normally distributed error, nonnormally distributed endogenous regressors are therefore required. Monte Carlo simulations assess the finite sample performance of the proposed estimator and demonstrate its superiority to conventional instrumental variable estimation. A specific advantage of the proposed method is that the estimator is unbiased in dynamic panel models with small time dimensions and serially correlated errors; therefore, it is a useful alternative to GMM-style instrumentation. The practical applicability of the proposed method is demonstrated via an empirical example.

scholarly journals Robust Bayesian Regression with Synthetic Posterior Distributions

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 661 ◽  
Author(s):  
Shintaro Hashimoto ◽  
Shonosuke Sugasawa
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Bayesian Variable Selection ◽  
Bayesian Regression ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Linear Regression Models ◽  
Computation Algorithm ◽  
Shrinkage Priors ◽  
Variable Selection And Estimation

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on γ-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

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